Case <- 100 시나리오 갯수
Ini.Stock<-100 초기 주가
StrikePrice<-100 옵션 행사 가격
year<- 10 년도
unit<- 12 단위 (12: 12개월, 365, 365일)
interval <- year X unit (구간의 갯수)
t <- 1/unit 년도를 구간으로 나눠준 수 r <-0.03
sigma<-0.2
mu <- r-0.5 X sigma^2
Bermuda.Start <- 50
Bermuda.End <- 110 버뮤다의 마지막 구간은 interval과 같거나 작아야함.
Bermuda_option <-function(CallorPut,Case,Ini.Stock,StrikePrice,year,unit,r,sigma,Bermuda.Start,Bermuda.End){
interval <- year * unit
t <- 1/unit
mu <- r-0.5*sigma^2
set.seed(5)
rnd.num <- as.data.frame(matrix(rnorm(Case*interval), nrow = Case, ncol=interval))
Yield.table <- as.data.frame(matrix(data = 0, nrow = Case, ncol = interval+1))
Payoff.table <- as.data.frame(matrix(data = 0, nrow = Case, ncol = interval))
Bermuda.table <- as.data.frame(matrix(data = 0, nrow = Case, ncol = 1))
if (CallorPut == 1){
for (i in 1:Case) {
for (j in 1:interval) {
Yield.table[i,j+1] <- Yield.table[i,j] + (mu*t+(sigma*sqrt(t)*rnd.num[i,j]))
Payoff.table[i,j] <- exp(-r*j/unit)*max(0,Ini.Stock*exp(Yield.table[i,j+1])-StrikePrice)
}}} else if (CallorPut == 2){
for (i in 1:Case) {
for (j in 1:interval) {
Yield.table[i,j+1] <- Yield.table[i,j] + (mu*t+(sigma*sqrt(t)*rnd.num[i,j]))
Payoff.table[i,j] <- exp(-r*j/unit)*max(0,StrikePrice-Ini.Stock*exp(Yield.table[i,j+1]))
}}} else { print("Call =1 , Put =2 로 설정해주셔야 합니다.")
}
if (Bermuda.End>0 & Bermuda.End<=interval){
for (i in 1:Case) {
Bermuda.table[i,1]<-max(Payoff.table[i,Bermuda.Start:Bermuda.End],Payoff.table[i,interval])
}
value<-mean(Bermuda.table[,1])
} else {value<-mean(Payoff.table[,interval])
}
return(value)
}
Bermuda_callop <-function(Case,Ini.Stock,StrikePrice,year,unit,r,sigma,Bermuda.Start,Bermuda.End){
interval <- year * unit
t <- 1/unit
mu <- r-0.5*sigma^2
set.seed(5)
rnd.num <- as.data.frame(matrix(rnorm(Case*interval), nrow = Case, ncol=interval))
Yield.table <- as.data.frame(matrix(data = 0, nrow = Case, ncol = interval+1))
Payoff.table <- as.data.frame(matrix(data = 0, nrow = Case, ncol = interval))
Bermuda.table <- as.data.frame(matrix(data = 0, nrow = Case, ncol = 1))
if (Bermuda.End>0 & Bermuda.End<=interval){
for (i in 1:Case) {
for (j in 1:interval) {
Yield.table[i,j+1] <- Yield.table[i,j] + (mu*t+(sigma*sqrt(t)*rnd.num[i,j]))
Payoff.table[i,j] <- exp(-r*j/unit)*max(0,Ini.Stock*exp(Yield.table[i,j+1])-StrikePrice)
}
Bermuda.table[i,1]<-max(Payoff.table[i,Bermuda.Start:Bermuda.End],Payoff.table[i,interval])}
value<-mean(Bermuda.table[,1])
} else {
for (i in 1:Case) {
for (j in 1:interval) {
Yield.table[i,j+1] <- Yield.table[i,j] + (mu*t+(sigma*sqrt(t)*rnd.num[i,j]))
Payoff.table[i,j] <- exp(-r*j/unit)*max(0,Ini.Stock*exp(Yield.table[i,j+1])-StrikePrice)
}}
value<-mean(Payoff.table[,interval])
}
return(value)
}
Bermuda_putop <-function(Case,Ini.Stock,StrikePrice,year,unit,r,sigma,Bermuda.Start,Bermuda.End){
interval <- year * unit
t <- 1/unit
mu <- r-0.5*sigma^2
set.seed(5)
rnd.num <- as.data.frame(matrix(rnorm(Case*interval), nrow = Case, ncol=interval))
Yield.table <- as.data.frame(matrix(data = 0, nrow = Case, ncol = interval+1))
Payoff.table <- as.data.frame(matrix(data = 0, nrow = Case, ncol = interval))
Bermuda.table <- as.data.frame(matrix(data = 0, nrow = Case, ncol = 1))
if (Bermuda.End>0 & Bermuda.End<=interval){
for (i in 1:Case) {
for (j in 1:interval) {
Yield.table[i,j+1] <- Yield.table[i,j] + (mu*t+(sigma*sqrt(t)*rnd.num[i,j]))
Payoff.table[i,j] <- exp(-r*j/unit)*max(0,StrikePrice-Ini.Stock*exp(Yield.table[i,j+1]))
}
Bermuda.table[i,1]<-max(Payoff.table[i,Bermuda.Start:Bermuda.End],Payoff.table[i,interval])}
value<-mean(Bermuda.table[,1])
} else {
for (i in 1:Case) {
for (j in 1:interval) {
Yield.table[i,j+1] <- Yield.table[i,j] + (mu*t+(sigma*sqrt(t)*rnd.num[i,j]))
Payoff.table[i,j] <- exp(-r*j/unit)*max(0,StrikePrice-Ini.Stock*exp(Yield.table[i,j+1]))
}}
value<-mean(Payoff.table[,interval])
}
return(value)
}
European_callop <-function(Case,Ini.Stock,StrikePrice,year,unit,r,sigma){
interval <- year * unit
t <- year/interval
mu <- r-0.5*sigma^2
set.seed(5)
#시뮬레이션 난수 값을 고정시키려면 set.seed(10) <10은 page와 같음> 10페이지에 있는 난수값.
rnd.num <- as.data.frame(matrix(rnorm(Case*interval), nrow = Case, ncol=interval))
Yield.table <- as.data.frame(matrix(data = 0, nrow = Case, ncol = interval+1))
Payoff.table <- as.data.frame(matrix(data = 0, nrow = Case, ncol = interval))
European.table <- as.data.frame(matrix(data = 0, nrow = Case, ncol = 1))
for (i in 1:Case) {
for (j in 1:interval) {
Yield.table[i,j+1] <- Yield.table[i,j] + (mu*t+(sigma*sqrt(t)*rnd.num[i,j]))
Payoff.table[i,j] <- exp(-r*j/unit)*max(0,Ini.Stock*exp(Yield.table[i,j+1])-StrikePrice)
}
European.table[i,1]<-Payoff.table[i,interval]
}
value<-mean(European.table[,1])
return(value)
}
European_putop <-function(Case,Ini.Stock,StrikePrice,year,unit,r,sigma){
interval <- year * unit
t <- year/interval
mu <- r-0.5*sigma^2
set.seed(5)
#시뮬레이션 난수 값을 고정시키려면 set.seed(10) <10은 page와 같음> 10페이지에 있는 난수값.
rnd.num <- as.data.frame(matrix(rnorm(Case*interval), nrow = Case, ncol=interval))
Yield.table <- as.data.frame(matrix(data = 0, nrow = Case, ncol = interval+1))
Payoff.table <- as.data.frame(matrix(data = 0, nrow = Case, ncol = interval))
European.table <- as.data.frame(matrix(data = 0, nrow = Case, ncol = 1))
for (i in 1:Case) {
for (j in 1:interval) {
Yield.table[i,j+1] <- Yield.table[i,j] + (mu*t+(sigma*sqrt(t)*rnd.num[i,j]))
Payoff.table[i,j] <- exp(-r*j/unit)*max(0,StrikePrice-Ini.Stock*exp(Yield.table[i,j+1]))
}
European.table[i,1]<-Payoff.table[i,interval]
}
value<-mean(European.table[,1])
return(value)
}
Bermuda_option(3,100,100,100,5,12,0.01,0.1,0,0)
[1] "Call =1 , Put =2 로 설정해주셔야 합니다."[1] 0Bermuda_option(2,100,100,100,5,12,0.02,0.1,0,0)
[1] 2.920645Bermuda_option(1,100,100,80,5,12,0.03,0.1,0,0)
[1] 33.56165Bermuda_callop(100,100,80,5,12,0.02,0.2,20,40)
[1] 54.56337Bermuda_putop(100,100,100,5,12,0.01,0.1,0,0)
[1] 4.413762European_callop(100,100,100,5,12,0.01,0.1)
[1] 11.41853European_putop(100,100,100,5,12,0.01,0.1)
[1] 4.413762knitr::opts_chunk$set(echo = TRUE)
If you want to get the plots about bermuda options, Write this down.
result.table.r<-c(1:100) result.table.sigma<-c(1:100) result.table.StrikePrice<-c(1:100) result.table.r2<-c(1:100) result.table.sigma2<-c(1:100) result.table.StrikePrice2<-c(1:100) sample.r<- seq(0.01,0.03,length.out = 100) sample.sigma<-seq(0.1,0.3,length.out = 100) sample.StrikePrice<-seq(80,120,length.out = 100)
for (i in 1:100) { result.table.r[i]<-Bermuda_option(1,100,100,100,5,12,sample.r[i],0.2,20,40) result.table.sigma[i]<-Bermuda_option(1,100,100,100,5,12,0.02,sample.sigma[i],20,40) result.table.StrikePrice[i]<-Bermuda_option(1,100,100,sample.StrikePrice[i],5,12,0.02,0.2,20,40) result.table.r2[i]<-Bermuda_option(1,100,100,100,5,12,sample.r[i],0.2,0,0) result.table.sigma2[i]<-Bermuda_option(1,100,100,100,5,12,0.02,sample.sigma[i],0,0) result.table.StrikePrice2[i]<-Bermuda_option(1,100,100,sample.StrikePrice[i],5,12,0.02,0.2,0,0)
}
plot(sample.r,result.table.r,type = “l”,col=“red”,xlab = “무위험이자율”,ylab=“콜옵션 가격”,xlim=c(0.009,0.031),ylim=c(10,50)) lines(sample.r,result.table.r2,type = “l”) legend(0.026,48,c(“European”,“Bermuda”),col=c(“black”,“red”),lty=1,cex=0.9)
plot(sample.sigma,result.table.sigma,type = “l”,col=“red”,xlab = “표준편차(시그마)”,ylab=“콜옵션 가격”,xlim=c(0.05,0.40),ylim=c(10,50)) lines(sample.sigma,result.table.sigma2,type = “l”) legend(0.32,49,c(“European”,“Bermuda”),col=c(“black”,“red”),lty=1,cex=0.9)
plot(sample.StrikePrice,result.table.StrikePrice,type = “l”,col=“red”,xlab = “행사가격”,ylab=“콜옵션 가격”,xlim=c(75,125),ylim=c(10,50)) lines(sample.StrikePrice,result.table.StrikePrice2) legend(114,49,c(“European”,“Bermuda”),col=c(“black”,“red”),lty=1,cex=0.9)
Initial Investment = I
CASHFLOW before tax = CF
Growth rate = G
Tax rate = T Cost of Captial = C
Period = N
library("dplyr")
NPVRAM <-function(I,CF,G,T,C,N) {
PVCF = 0
ACF= CF*(1-T) ##After tax cash flow
for(i in 1:N){
PVCF[i]<-ACF*(1+G)^(i-1) / (1+C)^i
}
sum(PVCF)-I}
### Monte Function ###
Monte <- function(PROB,RV) {if(PROB<=0.25){
return(RV[1])}
else if(PROB<=0.75) {
return(RV[2])
}
else {
return(RV[3])
}}
NPVRAM(5000000,1000000,0.03,0.25,0.06,10)
[1] 1239103A<-c(5500000,5000000,4500000)
B<-c(900000,1000000,1100000)
C<-c(0.02,0.03,0.04)
D<-c(0.35,0.25,0.15)
E<-c(0.07,0.06,0.05)
F<-c(8,10,12)
Result<-0
### NPVMONTE function ###
NPVMONTE <- function(x) {
NPV1<-c(1:x)
for(i in 1:x){
I1<-Monte(runif(1),A)
CF1<-Monte(runif(1),B)
G1<-Monte(runif(1),C)
T1<-Monte(runif(1),D)
C1<-Monte(runif(1),E)
N1<-Monte(runif(1),F)
NPV1[i] <- NPVRAM(I1,CF1,G1,T1,C1,N1)
}
return(NPV1)
}
Result1<-NPVMONTE(10000)
mean(Result1) ## NPV ???հ?
[1] 1224460var(Result1) ## NPV var ??
[1] 1.331364e+12Result1<-as.data.frame(Result1)
colnames(Result1) <- "NPV"
Result1<-arrange(Result1,NPV)
Positive<- filter(Result1,NPV>0)
nrow(Positive)/nrow(Result1) ## NPV ?? ?????? Ȯ?? ##
[1] 0.8519AM<- filter(Result1,NPV>1000000) ## Above 1Million
BM<- filter(Result1,NPV<1000000) ## Below 1Million
nrow(AM)/nrow(Result1) ## NPV 1,000,000 ?ʰ??? Ȯ??
[1] 0.5492[1] 0.4508Result1[100,1] ## 1 percentile ##
[1] -1091259Result1[1000,1] ## 10 percentile ##
[1] -209591.2Result1[9000,1] ## 90 percentile ##
[1] 2786013